Characterization of small abdominal aortic aneurysms' growth status using spatial pattern analysis of aneurismal hemodynamics

Aneurysm hemodynamics is known for its crucial role in the natural history of abdominal aortic aneurysms (AAA). However, there is a lack of well-developed quantitative assessments for disturbed aneurysmal flow. Therefore, we aimed to develop innovative metrics for quantifying disturbed aneurysm hemodynamics and evaluate their effectiveness in predicting the growth status of AAAs, specifically distinguishing between fast-growing and slowly-growing aneurysms. The growth status of aneurysms was classified as fast (≥ 5 mm/year) or slow (< 5 mm/year) based on serial imaging over time. We conducted computational fluid dynamics (CFD) simulations on 70 patients with computed tomography (CT) angiography findings. By converting hemodynamics data (wall shear stress and velocity) located on unstructured meshes into image-like data, we enabled spatial pattern analysis using Radiomics methods, referred to as "Hemodynamics-informatics" (i.e., using informatics techniques to analyze hemodynamic data). Our best model achieved an AUROC of 0.93 and an accuracy of 87.83%, correctly identifying 82.00% of fast-growing and 90.75% of slowly-growing AAAs. Compared with six classification methods, the models incorporating hemodynamics-informatics exhibited an average improvement of 8.40% in AUROC and 7.95% in total accuracy. These preliminary results indicate that hemodynamics-informatics correlates with AAAs' growth status and aids in assessing their progression.


A. Intensity-based Hemodynamics-informatics Features
The descriptions below are similar to that provided in PyRadiomics documentation and are provided below for completeness.

A.1 First-Order Statistics
First-order statistics features represent the distribution of distinct voxel values without considering the interrelationship with neighboring voxels. These histogram-based properties identify the mean, median, maximum, and minimum values of the voxel intensities on the image-like hemodynamic data and their asymmetry, flatness, uniformity, and entropy.

A.2 Second-Order Statistics:
In contrast, second-order statistics is related to information regarding the inter-relationship between neighboring voxel intensities and their spatial arrangement. Several methods that can quantify the voxels' inter-relationship have been reported, namely, Gray level co-occurrence matrix (GLCM) 1 , Gray level run length matrix (GLRLM) 2 , and Gray level size zone matrix (GLSZM) 3 . Parameters derived from GLCM, GLRLM, and GLSZM are summarized below.
To better comprehend voxels' inter-relationship analysis, graphical examples are provided below. In the examples below, we use images with discrete intensity values ranging from 1 to 5, and, as a result, each intensity value corresponds to one unique color.

A.2.1 Gray level co-occurrence matrix (GLCM)
Gray level co-occurrence matrix (GLCM) is computed based on the relationship between two connected voxels and the commonness of this connection and defined as ( , |δ, ). This relationship is represented using two components, distance (δ) and angle between two voxels , as shown in Fig. A.1(a). is one of four discrete values for 2D images, and this number increase to 13 for 3D images. Mathematically, the GLCM of an image (or image-like data) with Nx ×Ny dimensions and Ng different intensity levels is computed using the following    Maximum Probability: Quantifies the number of the most common set of adjacent intensity levels.
Sum Average: Estimates the association between the occurrences of connected pixels with lower and higher intensity levels. Here, , where i+j= and =2,3, …, 2Ng Sum Entropy: Aggregates of neighborhood intensity values distinctions.

A.2.2 Gray level run length matrix (GLRLM)
Gray level run length matrix (GLRLM) 2 is computed based on the number of connected voxels in the same intensity. GLRLM is characterized by an angle between pairs of voxels, . Elements (i,j) in the matrix represents the number of voxels with intensity i and run length j in a specified direction.
GrayLevelVariance: Measures variance of intensity level based on existing zones.
Here, μ = ∑ ∑ P(i, j|θ) j Zone Entropy: Quantifies the texture's coarseness based on the ratio between number of zones and number of voxels.
Zone Entropy = Here, N z represents the number of zones in ROI and is calculated as follows:

A.3 Higher-order statistics
Higher-order statistics features are computed using statistical methods after utilizing a filter or mathematical transform on the original image. The primary purpose of applying these techniques is to cancel noise, highlight detail, and identify repetitive and non-repetitive patterns. Including current existing techniques, we implemented the LoG filter, which can increasingly highlight coarse texture patterns and wavelet transform (WT) analyses image texture at different levels.

A.3.1 Laplacian of Gaussian (LoG) Filter
The Laplacian filter applies to the image to detect rapid changes in intensity levels, but this procedure is susceptible to noise. Therefore, the Gaussian filter is first applied to obtain a smooth image before the Laplacian filter. The above-mentioned two combined steps are known as the Laplacian of Gaussian (LoG) filter and aim at reducing the image noise level, improving the measurement of image heterogeneity 5 .

A.3.2 Wavelet transforms
Original Image WT is a mathematical technique to decompose original images into different sub-bands levels for generating multi-resolution images. Hence, WT can help to extract hidden information from an image 3,6-9 .
To start this process, one of these filter types is first applied to the original image on the x-axis. Then, one highpass and one low-pass image are obtained, labeled as H and L, respectively. Then, this process repeats in the y- An example of this process is depicted in Fig. A.5, in which coif1 with level 1 is applied on a 2D DWSS image.
A 3D image has one more step, and a WT needs to be applied to the z-axis on these four sub bands. As a result, we obtain HLL, HLH, HHH, HHL (high-pass along the z-axis) and LHL, LHH, LLH, LLL (loss-pass along the z-axis) images. By continually applying WT on LLL in 3D and LL in 2D images at each level, images with distinct resolution levels can be generated 4,11,12 .